Outlier Detection In Meta Regression Model

Meta-analysis is a systematic evaluation research method that quantitatively synthesizes multiple independent results of the same problem research based on statistical models.It is widely used in medicine,sociology,psychology,biology,ecology,economics and management and other fields.The core idea of meta-analysis is to integrate and comprehensively analyze multiple research results of the same problem as effect size in order to give more accurate quantitative inference results.The calculation model of comprehensive effect size in meta-analysis mainly includes fixed effect model and random effect model,in which the random effect model takes the existence of heterogeneity into account,so it is more valuable;and the parameter estimation of random effect meta-regression model that explains the heterogeneity is sensitive to the existence of outliers,so the problem of outlier detection is an important research content in meta-analysis.From the existing researches on outlier detection of meta-regression model,there are some shortcomings: first,there is less literature on how to deal with outliers;second,most papers only consider the problem of single outlier detection;finally,the statistical construction of statistical diagnosis in meta-regression ignores taking the interference of outliers on the estimation of heterogeneity parameters into consideration.Because the estimation of meta regression model involves iterative calculation,traditional statistical diagnosis usually adopts one-step approximate estimation method simply and directly to obtain approximate impact measurement and outlier test statistics.This method is equivalent to first fix the heterogeneous parameters and then derive the diagnostic statistics,and then substitute the estimation of the heterogeneous parameters with complete data.However,the between-study variance,namely the heterogeneity parameter,is also an important parameter in the meta-analysis.If the outliers have great influence on the heterogeneous parameters,the simple and direct one-step approximate estimation method will have great influence on the statistical diagnosis effect.Therefore,this paper systematically studies the statistical diagnosis of meta-analysis from a new perspective of the simultaneous effect of outliers on heterogeneous parameters and regression coefficient estimation.Firstly,a random effect meta-regression mean shift model is constructed to multiple outliers' detection.Taking the simultaneous influence of outliers on both the estimation of heterogeneous parameters and regression coefficient estimation into consideration,based on the LR test statistics of one-step approximate estimation,a new approximate estimation method is proposed.It makes up the defect that simple and direct one-step approximate estimation method that it is very difficult to construct test statistics accurately in statistical diagnosis.The simulation studies show that the power values of LR test statistics of the new approximate estimation method are higher than that of the one-step approximate estimation method.The comparative analysis of single or multiple outliers test results of two different types effect for meta-analysis real examples show that the new approximate estimation method has better recognition effect.In addition,based on single outlier detection and pair outliers detection results,an outlier modified model in terms of random effect meta regression mean shift(MSOMM)is constructed,it can effectively improve the model fitting effect,and empirical analysis of MSOMM can effectively improve its fitting effect.It provides a new idea for dealing with outliers in complex data models in real applications.Secondly,a random effect meta-regression variance weight model is constructed to multiple outliers detection.The SC test statistics of three perturbations in the random effect meta-regression model are derived,namely global variance perturbation,between-study variance perturbation and random error perturbation,it is proved that the SC test statistics of three kinds of variance perturbations are equal.Based on outliers detection results,taking the simultaneous influence of outliers on both the estimation of heterogeneous parameters and regression coefficient estimation into consideration,a random effect meta regression variance weight outlier modified model(VWOMM)is proposed,and the ML and REML estimation iterative algorithms for VWOMM model parameters are derived by numerical method.Random simulation verifies the size and power of SC test statistics.The outlier recognition results of two real examples with different types effect show that the constructed test statistics have significant recognition effects.At the same time,VWOMM can effectively improve the model fitting.It provides a new method for dealing with outliers of complex data models.Finally,the equivalence condition of case deletion,replacement and mean shift in statistical diagnosis of random effect meta regression model is discussed.Taking the simultaneous influence of outliers or influential observations on both the estimation of heterogeneous parameters and regression coefficient estimation into consideration,using ML and REML estimation,it studies the update iterative formula of regression coefficient for three statistical diagnostic methods of random effect meta-regression model: case deletion method,replacement method and mean shift model when the heterogeneous parameters are known and unknown,and the statistical diagnostic equivalence and mutual equivalence conditions of case deletion model,replacement model and mean shift model are obtained from the new perspective of meta-analysis.It demonstrates that the case deletion model,replacement model and mean shift model in the meta-analysis are equivalent when heterogeneous parameters are known,and the condition of mutual equivalence when heterogeneous parameters are unknown.In addition,the rate of change statistics as well as the Cook distance statistics of the regression coefficient and heterogeneous parameters of random effect meta regression model are constructed,and contrast verification is carried out with an example based on multiple outliers detection or influential observations.